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<h1>Eigenfunctions</h1>
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<h2>Characteristic equation</h2>
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<p>The characteristic equation of the n by n matrix A is A quantitative equation that contains useful information about the eigenvalues. The numerical equation det(A- λI) is called the characteristic equation of A, and λ is the eigenvalue of the matrix A if λ is the root of the characteristic equation det(A- λI)=0.</p>
<p> Solve the characteristic equation of matrix </p>
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<p>Characteristic equation is:</p>
<p align="center" ><b>(5-λ)^2*(3-λ)*(1-λ) = 0</b></p>
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<h2>Characteristic polynomial</h2>
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<p> det(A-λI) is called the characteristic polynomial of A.</p>
<p>Since the factor (5-λ) appears twice in the characteristic polynomial, the eigenvalue 5 has a multiplicity of 2. In general, the multiplicity of the eigenvalue as the root of the characteristic equation is called the λ multiplicity. </p>
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